Modern microlithography systems and other systems that require extremely accurate positioning of workpieces typically employ stages to hold and move the workpieces. For example, a microlithography system usually employs a stage for the lithographic substrate (e.g., semiconductor wafer, glass plate, or the like). If the lithography is performed based on a pattern defined by a reticle, then the microlithography system generally also includes a reticle stage. These stages generally provide motions in multiple orthogonal axes (x-, y-, z-directions), and may also include one or more tilting motions (θx, θy, θz). To meet current demands of accuracy and precision of stage motion, linear actuators are frequently used for producing stage motions. An exemplary linear actuator is a linear motor. Another type of electromagnetic actuator that can be used is a planar actuator such as a planar motor.
A typical linear actuator includes a stationary member and a moving member that moves relative to the stationary member. In linear motors one of these members comprises a plurality of permanent magnets arranged in a generally linear array along a principal axis of travel (principal “stroke axis”) of the actuator. The magnets are typically arranged with adjacent magnets having alternating polarity. The other member comprises an array of one or more electrical windings or “coils.” Either member can be the coil array or the magnet array. The magnetic fields produced by the magnet array interact with magnetic fields produced by electrical current flowing in the coil array to impart a linearly translational force to the moving member relative to the stationary member along the principal stroke axis. To a first approximation, this output force in the principal stroke axis is substantially linearly proportional to the current through the coil array.
Planar motors are types of linear actuators that produce movement within a defined plane, such as an x-y plane. Planar actuators have certain features that are similar to corresponding features in linear actuators. For example, in many planar motors, multiple permanent magnets are arranged in a two-dimensional array (rather than a one-dimensional array) on a platen serving as the stationary member, with a coil assembly serving as the moving member that moves relative to the stationary member. Planar actuators provide motion along a second orthogonal axis in addition to motion along a first orthogonal axis. Hence, a planar actuator may have, for example, more than one principal stroke axis. Since a planar motor produces movement in at least two dimensions, it also can be used to produce movement in one dimension (e.g., x- or y-axis).
Certain linear actuators provide motion along a second axis in addition to motion along the principal stroke axis. This second-axis motion is usually limited in range compared to motion along the principal stroke axis. These types of linear actuators thus provide motions in two degrees of freedom and are called herein “2DOF” linear actuators. An exemplary 2DOF linear actuator has a principal stroke axis in the y-direction and also provides motion along the z-axis. Motion in the y-direction results from a y-force-command (uy(y)) to the actuator that produces a y-direction output force Fy(y). Similarly, motion in the z-direction results from a z-force-command (uz(y)) to the actuator that produces a z-direction output force Fz(y).
With electromagnetic actuators, force-commands for motions in particular respective directions do not result only in motions of the moving member in the particular desired directions; the moving member usually also experiences additional forces. These additional forces are usually relatively small, but in some applications they can have a significant adverse impact on the accuracy and precision of motion and positioning produced by the actuator. One of these additional forces is called “force-ripple,” which is a periodic variation in the force output to the moving member in the direction (e.g., the principal stroke direction) corresponding to the force-command. Force-ripple arises from any of several various causes such as irregularities and imperfections in the magnets, the coils, or other aspects of the actuator's construction. Another of these additional forces is called “side-force,” which is a periodic variation in the force output to the moving member in a direction that is normal to the direction corresponding to the force-command. Side-force results from magnetic-field interactions similar to those that cause force-ripple. Force-ripple and side-force can be manifest in each stroke direction of the linear actuator. For example, a 2DOF linear actuator having y- and z-stroke axes may exhibit respective force-ripple and side-force associated with each stroke direction.
The magnitude of these additional forces usually varies with position of the moving member, even if a constant current is being supplied as a force-command to the coil(s). In some applications, the impact of these additional forces is negligible. In other applications, such as certain microlithography-stage applications, these additional forces can cause significant problems in achieving imaging accuracy and fidelity.
Spatial control of the moving member of an actuator, and thus of a stage moved by the moving member, could be improved by identifying and compensating for force-ripple and side-forces. Some OEM suppliers of linear actuators, for example, address this issue by providing, for each actuator, a map of force-ripple and/or side-force as a function of position of the moving member in the principal stroke direction. The end-user of the actuator can utilize the map to supply current to the coil array in a controlled manner that provides at least some offset to the force-ripple and/or side-force. In the map, each of a series of positions of the moving member in the principal stroke direction is associated with a respective offset of the respective force-ripple and/or side-force at the position. These maps, if provided, are conventionally produced during testing of the newly manufactured actuators by the manufacturer in a standard test environment. A disadvantage of these maps is that they are produced only at the time of manufacture of the respective actuators. The maps do not, and cannot, reflect variables introduced during actual installation and use of the actuators. Also, performance parameters of electromagnetic actuators usually change (e.g., drift) over time. These drifts and changes eventually render useless any compensations based on map data obtained when the actuators were new.
Therefore, there is a need for methods for identifying and compensating force-ripples and side-forces in electromagnetic actuators that can be performed substantially at any time, particularly in situ.